The sum of two numbers is $90$, and their difference is $18$. What are the two numbers?
Answer: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 90}$ ${x-y = 18}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 108 $ $ x = \dfrac{108}{2} $ ${x = 54}$ Now that you know ${x = 54}$ , plug it back into $ {x+y = 90}$ to find $y$ ${(54)}{ + y = 90}$ ${y = 36}$ You can also plug ${x = 54}$ into $ {x-y = 18}$ and get the same answer for $y$ ${(54)}{ - y = 18}$ ${y = 36}$ Therefore, the larger number is $54$, and the smaller number is $36$.